Lithographic apparatuses can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, the mask may contain a circuit pattern corresponding to an individual layer of the IC, and this pattern can be imaged onto a target portion (e.g. comprising one or more dies) on a substrate (silicon wafer) that has been coated with a layer of radiation-sensitive material (resist). In general, a single wafer will contain a whole network of adjacent target portions that are successively irradiated via the projection system, one at a time. In one type of lithographic projection apparatus, each target portion is irradiated by exposing the entire mask pattern onto the target portion in one go; such an apparatus is commonly referred to as a wafer stepper. In an alternative apparatus, commonly referred to as a step-and-scan apparatus, each target portion is irradiated by progressively scanning the mask pattern under the projection beam in a given reference direction (the “scanning” direction) while synchronously scanning the substrate table parallel or anti-parallel to this direction. Since, in general, the projection system will have a magnification factor M (generally <1), the speed V at which the substrate table is scanned will be a factor M times that at which the mask table is scanned. More information with regard to lithographic devices as described herein can be gleaned, for example, from U.S. Pat. No. 6,046,792, incorporated herein by reference.
The manufacturing process of an integrated circuit involves imaging multiple layers of circuit patterns onto a semiconductor wafer. To address the increasingly demanding needs of the semiconductor industry where the dimensions of the circuit elements are continually being reduced, technologies such as customized illumination schemes, phase shifting masks, and optical proximity correction (OPC) may be used. Numerical methods known as “computational lithography” are often required to simulate the lithography process to ensure the printed patterns meet the design target and to keep experimental costs under control. It is desirable that these numerical methods be highly accurate in order to predict the changes in aerial images (AIs) and critical dimensions (CDs) caused by small perturbations, also known as “sensitivities”, to the optical settings.
In a lithography simulation system, the optical properties of the scanner optics need to be characterized such that the aerial image of the mask within the resist layer is predicted correctly. In most applications, the optical system is modeled using model parameters, which are translated into mathematical coefficients or terms that are used in performing computational lithography. Generally, using a limited number of terms will increase system throughput, yet introduce more error in simulation and less reliable results. Accordingly, there is a need for methods that allow for fewer terms to be used, while retaining sufficient accuracy.